{"id":"74eb6136-8941-44cf-82a6-aa9243800592","arxiv_id":"2411.15083","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"VQE simulations of 0+1 dimensional supersymmetric quantum mechanics show that shot noise can mimic spontaneous supersymmetry breaking, and that a general-purpose ansatz fails for larger bosonic truncations.","lead":"The authors encode a simple supersymmetric quantum mechanics model into qubits and run variational quantum eigensolver (VQE) simulations on IBM's Qiskit simulators. Their main finding is that sampling noise from a finite number of shots can create a false signal of supersymmetry breaking, a caution for near-term hardware experiments.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central caution about shot noise mimicking SUSY breaking rests on the qualitative observation that HO VQE medians are 'consistent with a non-zero energy value' and increase with Λ; no numbers, confidence intervals, or significance tests are provided, so the effect is not yet quantitatively…","rationale":"I identify the missing statistical support for the HO shot-noise observation as the most load-bearing concern. The paper's strongest claim is the caution in Section 5 that shot noise can be misinterpreted as spontaneous SUSY breaking; the only evidence is the qualitative statement that shot-noise HO medians are 'consistent with a non-zero energy value, which tends to increase with larger Λ.' Everything downstream—the call for VQE users to account for shot noise—depends on that observation being real and significant. The paper reports no numbers, intervals, or tests, and Fig. 4 alone cannot establish significance of a median of 100 runs, especially since the termination point of each run is itself a noise-affected quantity. I considered two alternative primary objections and rejected them: (i) hardware fidelity (the reader's weakest_assumption) is a scoping limitation the authors explicitly acknowledge in the abstract and Section 6, so it does not attack the internal claim; (ii) the optimizer-attribution tension between Sections 5 and 6 is real but is itself part of the same missing-quantification problem. Credit where due: the statevector benchmarks against exact diagonalization for HO and DW are clean, the code is public (Ref. [17]), and the parameter count is minimal, which makes the proposed re-analysis straightforward and decisive. The reader's CONDITIONAL verdict already requires statistical quantification, and my concern reinforces rather than moves that verdict, so I recommend UNCHANGED. I mark agreement as partial because the reader's rationale mentions the missing quantification but their weakest_assumption field centers on hardware representativeness.","tokens_in":7343,"tokens_out":11729,"duration_ms":116988,"concrete_test":"Download the public code from Ref. [17], reproduce the 100 HO shot-noise VQE runs (10,000 shots, COBYLA, RealAmplitude) for Λ = 2, 4, 8, 16, 32, 64, and extract the 100 final energies per Λ. For each Λ, compute the median with a bootstrap 95% confidence interval (≥10^4 resamples) and run a one-sided Wilcoxon signed-rank test of the null median = 0; then test the trend with a Spearman correlation between Λ and the per-Λ medians. If any bootstrap CI includes zero or the trend is not significant at p < 0.05, the Section 5 observation is not established. As a secondary check that settles the optimizer-specificity question, rerun Λ = 16 with a different noise-tolerant optimizer (e.g., SPSA) at the same shot budget; if the positive median vanishes, the central caution is COBYLA-specific.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim—that finite-shot sampling noise can produce a spurious spontaneous-SUSY-breaking signal in VQE—rests on a single qualitative observation in Section 5: for the harmonic oscillator, the shot-noise median is 'consistent with a non-zero energy value, which tends to increase with larger Λ.' No numerical medians, interquartile ranges, bootstrap confidence intervals, or hypothesis tests are reported for the 100 runs, and the Λ-trend is asserted without a fit or a significance measure. The claim is not a trivial consequence of finite statistics: for a symmetric shot-noise error around the true value E0 = 0, the median of 100 noisy estimates would sit near zero, so a systematically positive, Λ-increasing median is a real empirical effect that must be established beyond visual inspection of Fig. 4. The missing quantification also leaves the mechanism ambiguous: Section 6 attributes the discrepancy to 'the COBYLA optimizer struggles to find the minimum in presence of noise,' which raises the possibility that the spurious signal is specific to the interaction of COBYLA with a noisy objective rather than a generic property of finite-shot VQE. If the median is within uncertainty of zero, or if the Λ-trend is not significant, the central caution loses its evidentiary basis. This objection concerns the internal support for the shot-noise claim, not its transfer to real hardware, which the authors explicitly scope out in Section 6.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings paper explores the use of the variational quantum eigensolver (VQE) to detect spontaneous supersymmetry breaking in 0+1-dimensional supersymmetric quantum mechanics. The authors encode the model on qubits using one fermionic qubit and B bosonic qubits for Λ=2^B bosonic modes, and study three superpotentials (harmonic oscillator, double well, anharmonic oscillator). For each case they perform 100 VQE runs on Qiskit statevector and shot-noise simulators using the RealAmplitude ansatz and the COBYLA optimizer, comparing the resulting ground-state energy distributions with exact diagonalization. The paper's main observation is that in the presence of shot noise the harmonic-oscillator median ground-state energy appears positive and increases with Λ, which could be misinterpreted as evidence of spontaneous supersymmetry breaking. The authors also provide a tabulation of the Pauli-string resources required for various truncations.","tokens_in":7586,"tokens_out":8527,"duration_ms":84129,"significance":"If the shot-noise caution is quantitatively established, it is a valuable practical warning for VQE-based studies of supersymmetry breaking on near-term quantum hardware, and the paper offers a clean, explicit qubit encoding and resource estimates for the SQM models. The statevector results benchmarked against exact diagonalization support the basic validity of the encoding and the VQE setup. However, the central claim about shot noise currently rests on qualitative inspection of boxplots without numerical values, confidence intervals, or significance tests, and the attribution to the COBYLA optimizer is not tested. The manuscript is explicitly preliminary, and the authors appropriately scope out hardware noise, but the evidentiary basis for the headline finding needs strengthening before it can be considered established.","major_comments":[{"comment":"The central claim that shot noise produces a spurious positive median ground-state energy for the harmonic oscillator is not quantified. The text states that \"the median is consistent with a non-zero energy value, which tends to increase with larger Λ,\" but no numerical medians, interquartile ranges, confidence intervals, or significance tests are reported for the 100 runs. Without these, the reader cannot determine whether the positive median is statistically significant or within the expected finite-sample fluctuation around the true value E0=0, and the Λ-trend is asserted without a fit or a correlation measure. Please report the numerical values and a simple statistical test (e.g., a bootstrap confidence interval for the median or a sign test against zero), and quantify the trend, for example with a rank correlation or a linear fit.","section":"Section 5, Fig. 4"},{"comment":"The paper attributes the shot-noise discrepancy to the statement that \"the COBYLA optimizer struggles to find the minimum in presence of noise.\" This leaves open the possibility that the positive median is an artifact of the specific interaction between COBYLA and a noisy objective rather than a generic property of finite-shot VQE. To support the general caution, please compare with at least one alternative optimizer (e.g., SPSA or a gradient-based method) under the same shot-noise conditions, or demonstrate the same positive shift with a fixed ansatz parameter set. If the effect is optimizer-specific, the conclusion should be reframed accordingly.","section":"Section 5, Fig. 4 and Section 6"}],"minor_comments":[{"comment":"Please clarify whether the vertical lines for the harmonic oscillator represent the exact diagonalization energy of the truncated Hamiltonian or the continuum result E0=0. Section 3 states that the bosonic truncation explicitly breaks supersymmetry, so it would be helpful to state explicitly how the truncated ED energy behaves for HO as Λ increases.","section":"Section 5, Fig. 4"},{"comment":"The description of the shot-noise simulations is ambiguous: \"10000 shot executions for each of the 100 VQE runs\" could mean 10,000 shots per Pauli string per energy evaluation or 10,000 shots total per run. Please specify the measurement budget, since the effective shot noise depends on this.","section":"Section 5"},{"comment":"For the anharmonic oscillator, the statevector VQE agrees with exact diagonalization only up to Λ=8, and the text acknowledges this. Please state explicitly in the conclusions that the current ansatz does not scale to larger bosonic truncations for the AHO, and clarify whether the failure is due to optimizer convergence or ansatz expressibility.","section":"Section 5, AHO results"},{"comment":"The caption contains a typo: \"different superpontentials\" should be \"different superpotentials.\"","section":"Figure 4 caption"},{"comment":"The text says \"the Λ states require B qubits, where Λ=2^B\"; the notation is correct, but consider adding a brief explanation of why B qubits are sufficient for Λ=2^B bosonic modes.","section":"Section 3"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, and the preliminary nature of the results is understandable. However, the central claim about shot noise mimicking supersymmetry breaking is not yet supported quantitatively; the missing statistics and optimizer comparison are essential before the claim can be accepted. The paper would be strengthened by reporting numbers for the boxplots and a test of the Λ-trend, as well as a robustness check with another optimizer."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a modest proceedings paper from an established program. The only genuinely new result is the observation that finite-shot sampling noise shifts VQE medians away from the exact zero energy in the harmonic oscillator, potentially mimicking spontaneous SUSY breaking. The statevector results match exact diagonalization across the board, and the code is public, so the baseline is solid. But the headline shot-noise claim is supported only by boxplots; no medians, errors, or significance tests are reported, and the authors themselves attribute the discrepancy to COBYLA's behavior under noise, which weakens the generality of the caution.\n\nWhat's new: prior papers by the same group [6,8,9] used noiseless statevector simulation. This one adds shot noise at 10,000 shots per run across 100 runs and shows the effect. That is a legitimate extension. The resource table with Pauli-string counts is a useful community service. I also credit the paper for its careful phrasing: it says noise \"might be misinterpreted,\" not that it definitively invalidates VQE, and Section 6 explicitly defers hardware noise.\n\nSoft spots, in proportion: the central claim lacks quantification. For the HO, the exact energy is zero, so a symmetric sampling error should center near zero. The assertion that the median is non-zero and grows with Lambda is a real empirical effect that needs numbers. A bootstrap confidence interval on the medians, or even a simple sign test, would settle it. This is the load-bearing result, and it is currently visual inspection of Fig. 4. I agree with the stress-test note that the mechanism is also ambiguous: the authors say COBYLA struggles in the presence of noise, which suggests the spurious signal may be optimizer-specific rather than a generic property of finite-shot VQE. Testing a second optimizer or at least adding a caveat would make the warning more robust. Minor: the AHO statevector results fail beyond Lambda=8, which they acknowledge; the DW shot-noise results are order-of-magnitude larger than the HO case, which supports their interpretation but is again not statistically formalized.\n\nOverall: this is what it claims to be, a preliminary study with an important caution for a niche community. The caution, if correct, affects how VQE results for SUSY models should be interpreted. The fix is straightforward: report numbers with confidence intervals, and ideally run a different optimizer. I would send it to peer review rather than desk-reject, expecting a moderate revision.","headline":"A modest but honest proceedings paper: the shot-noise caution is plausible and useful, but underquantified; the statevector baselines are solid and reproducible.","tokens_in":8149,"tokens_out":2017,"would_cite":false,"duration_ms":20945,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Sampling noise from a fixed number of shots can make a supersymmetry-preserving model appear to spontaneously break supersymmetry.","keywords":["supersymmetric quantum mechanics","variational quantum eigensolver","shot noise","spontaneous supersymmetry breaking","qubit encoding","lattice supersymmetry","quantum simulation","sign problem"],"falsifier":"Repeat the harmonic-oscillator VQE on real quantum hardware, or on a simulator that adds gate errors and decoherence, at shot counts from $10^3$ to $10^6$, and record the median ground-state energy as a function of $\\Lambda$. If the nonzero median disappears or does not grow with $\\Lambda$ when hardware noise is included, the paper's claim that shot noise alone can create a spurious supersymmetry-breaking signal would not hold on actual devices; if the bias persists and shrinks with increasing shots, the shot-noise explanation is confirmed.","tokens_in":7102,"feed_emoji":"⚛️","tokens_out":7618,"duration_ms":66837,"temperature":0.7,"pith_summary":"This proceedings article tests a quantum-computing route to a classic problem: deciding whether supersymmetric quantum mechanics preserves or spontaneously breaks supersymmetry, which is read off from whether the ground-state energy is zero or nonzero. The authors encode a 0+1-dimensional boson-fermion system on qubits and run the variational quantum eigensolver (VQE) on an exact noiseless simulator and on a simulator that includes the sampling noise of 10,000 shots. Their central finding is a caution: for the harmonic-oscillator superpotential, which exactly preserves supersymmetry and has zero ground-state energy, the shot-noise runs produce a median energy that is nonzero and grows with the bosonic truncation level, so a researcher looking only at the noisy results could wrongly report spontaneous supersymmetry breaking. They conclude that shot noise must be accounted for in future VQE studies, and they point to repeating runs at different shot counts and using variational quantum deflation as next steps.","feed_headline":"Shot noise can fake supersymmetry breaking in VQE","feed_subtitle":"In a 0+1D quantum-mechanics model, 10,000-shot VQE runs give the harmonic oscillator a nonzero median ground-state energy.","key_machinery":"The object carrying the argument is the supersymmetric quantum-mechanics Hamiltonian $H=\\frac{1}{2}(\\hat{p}^2+[W'(\\hat{q})]^2-W''(\\hat{q})\\,[\\hat{b}^\\dagger,\\hat{b}])$, whose supercharges satisfy $2H=\\{Q,Q^\\dagger\\}$; because every eigenenergy is non-negative, a zero-energy ground state exists exactly when both supercharges annihilate it, making the ground-state energy the order parameter for spontaneous supersymmetry breaking. The numerical machinery is VQE with a RealAmplitude ansatz, single-qubit rotations plus a reverse-linear chain of CNOT entanglers, minimized by the gradient-free COBYLA optimizer and run 100 times per superpotential and truncation level. The diagnostic that makes the noise visible is the boxplot of those 100 runs placed against the exact diagonalization value: the median, quartiles, and outliers turn a collection of noisy energy measurements into a clear visual statement that the noisy distribution is biased away from zero.","core_discovery":"The paper's central claim is that sampling noise, not physics, can masquerade as spontaneous supersymmetry breaking in current quantum-simulation workflows. For the harmonic-oscillator superpotential, exact diagonalization and a noiseless state-vector VQE both give ground-state energy zero for every truncation level $\\Lambda$, matching the expectation that supersymmetry is preserved. The VQE runs with 10,000 shots instead give a distribution of energies whose median is positive and increases with $\\Lambda$; by the model's standard criterion, nonzero ground-state energy means supersymmetry is spontaneously broken, so this looks like breaking. The authors state directly that this illustrates how noise from a fixed number of shots might be misinterpreted as evidence of spontaneous supersymmetry breaking. In the double-well case, where supersymmetry is genuinely broken, the larger energy scale makes the breaking signal survive the noise, while in the anharmonic-oscillator case bosonic truncation effects already make even the noiseless results deviate beyond $\\Lambda=8$.","pith_inferences":["The same spurious-breaking mechanism should apply to any VQE order parameter measured with finite shots and a noisy optimizer, so the caution generalizes beyond supersymmetry to symmetry-breaking searches in other lattice models.","A testable extension is to quantify how the median bias scales with shot count and truncation level for the harmonic oscillator; if the bias falls as the inverse square root of the shot count, it is purely sampling noise, while a plateau would indicate optimizer bias.","Comparing noiseless and shot-noise distributions, as the boxplots do, could become a standard low-cost diagnostic for detecting optimizer-versus-noise artifacts before moving to real hardware.","The truncation-plus-noise interplay seen in the anharmonic-oscillator model suggests that digitization errors and sampling noise may compound, motivating studies that vary both $\\Lambda$ and shot count simultaneously."],"forward_implications":["VQE studies that search for spontaneous supersymmetry breaking should report shot-count dependence, repeating runs at different numbers of shots, before interpreting a nonzero ground-state energy as breaking.","For the harmonic-oscillator superpotential, shot noise biases the median energy upward with increasing bosonic truncation $\\Lambda$, so noiseless-versus-noisy comparisons are needed to separate algorithmic bias from physical signals.","The double-well superpotential's spontaneous breaking signal is large enough to survive shot noise, so not all supersymmetry-breaking conclusions from VQE are suspect.","The general-purpose ansatz used here reproduces exact results only for modest $\\Lambda$, so reaching the untruncated limit will require a problem-tailored ansatz.","A more robust route is to compute the low-energy spectrum, for example with variational quantum deflation, rather than only the ground-state energy, since the pairing of excited states is a cleaner supersymmetry diagnostic."],"supporting_citations":[{"why":"introduces the variational quantum eigensolver, the algorithm whose noisy behavior this paper studies.","marker":"[5]"},{"why":"earlier VQE study of the same 0+1 dimensional model without shot noise; the omission this work addresses.","marker":"[6]"},{"why":"establishes the supersymmetric quantum-mechanics framework and the criterion that the superpotential shape controls spontaneous supersymmetry breaking.","marker":"[10]"},{"why":"supplies the bosonic digitization options and the truncation that makes the bosonic mode count $\\Lambda$ explicit.","marker":"[11]"},{"why":"provides the quantum-computing software used to construct the circuits and to count Pauli strings in Table 1.","marker":"[12]"},{"why":"the gradient-free optimizer whose interaction with sampling noise shapes the VQE energy distributions.","marker":"[18]"}],"fun_headline_variants":["Sampling noise can fake spontaneous SUSY breaking","Shot noise mimics supersymmetry breaking in VQE","Quantum noise tricks: false SUSY breaking signal","Sampling errors produce fake SUSY breaking in 0+1D"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The warning depends on the assumption that a simulator with 10,000 random samples and the chosen classical optimizer behaves like real quantum hardware; the paper explicitly leaves gate errors and decoherence for future work, so the caution has not yet been demonstrated on actual devices.","fun_headline_variants_meta":{"raw":{"variants":["Sampling noise can fake spontaneous SUSY breaking","Shot noise mimics supersymmetry breaking in VQE","Quantum noise tricks: false SUSY breaking signal","Sampling errors produce fake SUSY breaking in 0+1D"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000292,"raw_usage":{"total_tokens":1718,"prompt_tokens":973,"completion_tokens":745,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":589,"completion_tokens_details":{"reasoning_tokens":680}},"tokens_in":589,"tokens_out":745,"duration_ms":7561,"temperature":1.0,"reasoning_tokens":680,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:31:41.883129+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the harmonic-oscillator VQE on real quantum hardware, or on a simulator that adds gate errors and decoherence, at shot counts from $10^3$ to $10^6$, and record the median ground-state energy as a function of $\\Lambda$. If the nonzero median disappears or does not grow with $\\Lambda$ when hardware noise is included, the paper's claim that shot noise alone can create a spurious supersymmetry-breaking signal would not hold on actual devices; if the bias persists and shrinks with increasing shots, the shot-noise explanation is confirmed.","supporting_citations":[{"cited_title":"Quantum computing for lattice supersymmetry","cited_arxiv_id":"2112.07651","evidence_quote":"earlier VQE study of the same 0+1 dimensional model without shot noise; the omission this work addresses."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the gradient-free optimizer whose interaction with sampling noise shapes the VQE energy distributions."}],"review_version":1}